On the first twisted Dirichlet eigenvalue
نویسندگان
چکیده
In this paper we prove an isoperimetric inequality for the twisted Dirichlet eigenvalue which was introduced by Barbosa and Bérard in the context of constant mean curvature surfaces. More precisely, we show that in the Euclidean case this eigenvalue is minimized by the union of two equal balls.
منابع مشابه
An isoperimetric inequality for a nonlinear eigenvalue problem
We present an isoperimetric inequality for a nonlinear generalization of the first twisted Dirichlet eigenvalue. Let λ(Ω) be the set functional defined by λ(Ω) = inf { ‖∇v‖Lp(Ω) ‖v‖Lq(Ω) , v ∈W }
متن کاملA Second Eigenvalue Bound for the Dirichlet Laplacian in Hyperbolic Space
Let Ω be some domain in the hyperbolic space Hn (with n ≥ 2) and S1 the geodesic ball that has the same first Dirichlet eigenvalue as Ω. We prove the Payne-Pólya-Weinberger conjecture for Hn, i.e., that the second Dirichlet eigenvalue on Ω is smaller or equal than the second Dirichlet eigenvalue on S1. We also prove that the ratio of the first two eigenvalues on geodesic balls is a decreasing f...
متن کامل2 2 Ju n 20 04 The First Dirichlet Eigenvalue and the Li Conjecture ∗
We give a new estimate on the lower bound for the first Dirichlet eigenvalue for the compact manifolds with boundary and positive Ricci curvature in terms of the diameter and the lower bound of the Ricci curvature and give an affirmative answer to the conjecture of P. Li for the Dirichlet eigenvalue.
متن کاملFirst Eigenvalue of One-dimensional Diffusion Pro- Cesses
We consider the first Dirichlet eigenvalue of diffusion operators on the half line. A criterion for the equivalence of the first Dirichlet eigenvalue with respect to the maximum domain and that to the minimum domain is presented. We also describle the relationships between the first Dirichlet eigenvalue of transient diffusion operators and the standard Muckenhoupt’s conditions for the dual weig...
متن کاملA RESEARCH NOTE ON THE SECOND ORDER DIFFERENTIAL EQUATION
Let U(t, ) be solution of the Dirichlet problem y''+( t-q(t))y= 0 - 1 t l y(-l)= 0 = y(x), with variabIe t on (-1, x), for fixed x, which satisfies the initial condition U(-1, )=0 , (-1, )=1. In this paper, the asymptotic representation of the corresponding eigenfunctions of the eigen values has been investigated . Furthermore, the leading term of the asymptotic formula for ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2017